Question

the area of rectangle plot is 528 m square the length of the plot is more than twice its breadth we need to find the length and breadth of the plot

Answer 1

$\textbf{SOLUTION :}$

Given : Area of the rectangle = 528 m²

Let the breadth of the rectangle be x m

Length of the rectangle = (2x + 1) m

Area of the rectangle = l × b

(2x + 1) x x = 528

2x² + x - 528 = 0

2x² + 33x - 32x - 528 = 0

$\textbf{[By middle term splitting]}$

x(2x + 33) - 16(2x + 33) = 0

(x - 16) (2x + 33) = 0

(x - 16) or (2x + 33) = 0

x = 16 or x = - 33/2

Since, the breadth can't be negative, so x ≠ - 33/2  

Therefore , x = 16

breadth of the rectangle = x =  16 m

Length of the rectangle = 2x + 1 =  (2× 16 + 1) = 32 + 1 = 33 cm  

$\textbf{Hence, the length and the breadth of the plot is 33 cm & 16 cm.}$

$\textbf{HOPE THIS ANSWER WILL HELP YOU…..}$

Answer 2

Given: The length of rectangular plot is one more than twice it's breadth. & Area of park is 528 m².

Need to find: Dimensions of rectangular plot?

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's consider breadth of rectangular plot be x m.

Then, Length of rectangular plot is (2x + 1) m.

⠀⠀⠀⠀⠀

As we know that,

⠀⠀⠀⠀⠀

$\begin{gathered}\star\:{\underline{\boxed{\frak{Area_{\:(rectangle)} = Length \times Breadth}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 528 = x \times (2x + 1)\\\\\\ :\implies\sf 528 = 2x^2 + x\\\\\\ :\implies\sf 2x^2 + x - 528 = 0\\\\\\ :\implies\sf 2x^2 - 32x + 33x - 528 = 0\\\\\\ :\implies\sf 2x(x - 16) + 33(x - 16) = 0\\\\\\ :\implies\sf (2x + 33)(x - 16) = 0\\\\\\ :\implies\sf Either\:(2x + 33) = 0\:or\:(x - 16) = 0\\\\\\ :\implies{\underline{\boxed{\frak{\purple{ x = \dfrac{-33}{2}\:;\: 16}}}}}\:\bigstar\\\\\end{gathered}$

We know that,

Dimensions of rectangle can't be negative.

⠀⠀⠀⠀⠀

Hence, x = 16.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Therefore,

⠀⠀⠀⠀⠀

Breadth of rectangular park, x = 16 m

Length of rectangular park, (2x + 1) = 33 m

⠀⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:Dimensions\:of\:rectangular\:plot\:is\:\bf{16\:m}\: \sf{and}\: \bf{33\:m}\: \sf{respectively}.}}}$